MACM 101 Lecture 27: Lecture 27 Part 1_ Modular Arithmetic
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21 Dec 2018
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Congruences in some situations we care only about the remainder of an integer when it is divided by some specified positive number. For instance, when we ask what time it will be 50 hours from now, we care only about the remainder of 50 plus the current hour divided by 24. If a and b are integers and m is a positive integer, then a is congruent to b modulo m if m divides a b. We use the notation a b (mod m) to indicate that a is congruent to b modulo m. if a and are not congruent modulo m, we write a b (mod m) Integers a and b are congruent modulo m if and only if they have the same remainder when divided by m. Indeed, if a b = km and b = qm + r, then a = km + b = (k + q)m + r.
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